We propose a phase field model for simulating solid-state dewetting and the morphological evolution of patterned islands on a substrate. The evolution is governed by the Cahn–Hilliard equation with isotropic surface tension and variable scalar mobility. The proposed approach easily deals with the complex boundary conditions arising in the solid-state dewetting problem. Since the method does not explicitly track the moving surface, it naturally captures the topological changes that occur during film/island morphology evolution. The numerical method is based on the cosine pseudospectral method together with a highly efficient, stabilized, semi-implicit algorithm. Numerical results on solid-state dewetting in two dimensions demonstrate the excellent performance of the method, including stability, accuracy and numerical efficiency. The method was easily extended to three dimensions (3D), with no essential difference from the two-dimensional algorithm. Numerical experiments in 3D demonstrate the ability of the model to capture many of the complexities that have been observed in the experimental dewetting of thin films on substrates and the evolution of patterned islands on substrates.